Planetary waves in a stratified ocean of variable depth. Part 2. Continuously stratified ocean

Linear Rossby waves in a continuously stratified ocean over a corrugated rough-bottomed topography are investigated by asymptotic methods. The main results are obtained for the case of constant buoyancy frequency. In this case there exist three types of modes: a topographic mode, a barotropic mode, and a countable set of baroclinic modes. The properties of these modes depend on the type of mode, the relative height delta of the bottom bumps, the wave scale L, the topography scale L-b and the Rossby scale L-i. For small delta the barotropic and baroclinic modes are transformed into the 'usual' Rossby modes in an ocean of constant depth and the topographic mode degenerates. With increasing delta the frequencies of the barotropic and topographic modes increase monotonically and these modes become close to a purely topographic mode for sufficiently large delta. As for the baroclinic modes, their frequencies do not exceed O(beta L) for any delta. For large delta the so-called 'displacement' effect occurs when the mode velocity becomes small in a near-bottom layer and the baroclinic mode does not 'feel' the actual rough bottom relief. At the same time, for some special values of the parameters a sort of resonance arises under which the large- and small-scale components of the baroclinic mode intensify strongly near the bottom. As in the two-layer model, a so-called 'screening' effect takes place here. It implies that for L-b much less than L-i the small-scale component of the mode is confined to a near-bottom boundary layer (L-b/L-i)H thick, whereas in the region above the layer the scale L of motion is always larger than or of the order of L-i.